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<p>In this paper, we propose two novel rational forms of multiplicative inverse cubic functional equations. We extended these equations to multicubic reciprocal functional equations and determined their general solutions in restricted domains. Furthermore, we demonstrate that in the context of non-Archimedean spaces, the stability results of these equations relevant to the Ulam-Hyers stability theory remain valid. The stability result pertinent to Rassias stability and a suitable example for a non-stability result are also demonstrated. The approximation error and its sharpness are also found for the stability result. The stability result is illustrated through a numerical example. The results are compared with the classical cubic functional equation. The equations addressed in this article are interpreted with an application to the volume of regular tetrahedrons with different heights through the triangle-Cevian concept.</p>

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Solutions and approximations of a system of cubic reciprocal functional equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月20日

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  • Abasalt Bodaghi,
  • Beri Venkatachalapathy Senthil Kumar

摘要

In this paper, we propose two novel rational forms of multiplicative inverse cubic functional equations. We extended these equations to multicubic reciprocal functional equations and determined their general solutions in restricted domains. Furthermore, we demonstrate that in the context of non-Archimedean spaces, the stability results of these equations relevant to the Ulam-Hyers stability theory remain valid. The stability result pertinent to Rassias stability and a suitable example for a non-stability result are also demonstrated. The approximation error and its sharpness are also found for the stability result. The stability result is illustrated through a numerical example. The results are compared with the classical cubic functional equation. The equations addressed in this article are interpreted with an application to the volume of regular tetrahedrons with different heights through the triangle-Cevian concept.